We present the results of the Swift observations of the nearby BL Lac object Mrk421 during 2013 November-2015 June. The source exhibited a strong long-term variability in the 0.3-10keV band, with a maximum-to-minimum flux ratio of 13, and underwent X-ray flares by a factor of 1.8-5.2 on timescales of a few weeks or shorter. The source showed 48 instances of intraday flux variability in this period, which sometimes was observed within the 1 ks observational run. It was characterized by fractional amplitudes of 1.5(0.3)%-38.6(0.4)% and flux doubling/halving times of 2.6-20.1hr. The X-ray flux showed a lack of correlation with the TeV flux on some occasions (strong TeV flares were not accompanied by comparable X-ray activity and vice versa), indicating that the high-energy emission in Mrk421 was generated from an emission region more complex than a single zone. The best fits of the 0.3-10keV spectra were mainly obtained using the log-parabola model, showing a strong spectral variability that generally followed a "harder-when-brighter" trend. The position of the synchrotron spectral energy distribution peak showed an extreme range from a few eV to ~10keV that happens rarely in blazars.